In recent years, various important characteristics have been required for ink jet inks, for example, ink reliability (including ejection stability and ejection accuracy), image quality (including high optical density), and image fastness (including scratch resistance and highlighter resistance). In order to improve these characteristics, various pigment inks containing a polyurethane polymer have been studied (PTLs 1 to 4). PTL 1 discloses an aqueous ink jet ink that contains a dispersion of a polyurethane polymer having an acid group and a self-dispersing pigment. PTL 2 discloses a pigment dispersion that contains a polyurethane polymer, which contains a compound having three or more hydroxy groups and a soft segment having a carboxy group. The soft segment contains a polyol. PTL 3 discloses an aqueous pigment ink containing a polyurethane polymer in which the ratio of the urethane bond to the urea bond is specified. PTL 4 discloses an aqueous pigment ink that contains a polyurethane polymer having no urea bond.